The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.
An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz / D.MUNDICI; R.CIGNOLI. - In: STUDIA LOGICA. - ISSN 0039-3215. - STAMPA. - 58:(1997), pp. 79-97. [10.1023/A:1004991931741]
An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
MUNDICI, DANIELE;
1997
Abstract
The interpretation of propositions in Łukasiewicz's infinite-valued calculus as answers in Ulam's game with lies-the Boolean case corresponding to the traditional Twenty Questions game-gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.